Finite Group Databasebeta

← #14583545

Subgroups — #14583545

Order 2752.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10621898C211yesmaximal, characteristic, complemented
2C22×D172C211yesmaximal, characteristic, complemented
3#13063313C211yesmaximal, characteristic, complemented
4#13063310C212yesmaximal, complemented
5#13063304C211yesmaximal, characteristic, complemented
6#13063299C211yesmaximal, characteristic, complemented
7#13063298C212yesmaximal, complemented
8#13063293C212yesmaximal, complemented
9C4×D172C211yesmaximal, characteristic, complemented
10C22⋊C4×D43C212yesmaximal, complemented
11C4×D4×C43C211yesmaximal, characteristic, complemented
12C23×D43C2212yes—
13C2×D4×C43C2211yescharacteristic
14C22×C4×C43C2211yescharacteristic
15C22×C4×C43C2211yescharacteristic, complemented
16C2×C22⋊D43C2212yescomplemented
17C2×C22⋊D43C2212yescomplemented
18#10621898—24no—
19C2×D172—24no—
20C2×D172C2212yes—
21C2×D172C2211yescharacteristic
22C2×D172C2211yescharacteristic
23C2×C4×D43C2212yescomplemented
24C2×C4×D43C2212yescomplemented
25C2×Dic86C2211yescharacteristic, complemented
26C4⋊C4×C43C2211yescharacteristic, complemented
27C22⋊C4×C43C2211yescharacteristic
28C22⋊C4×C43C2211yescharacteristic, complemented
29C42×C43C2211yescharacteristic, complemented
30C22⋊Dic43C2212yes—
31(C2×D43)⋊C4C2212yescomplemented
32(C2×D43)⋊C4C2212yescomplemented
33(C2×D43)⋊C4C2212yescomplemented
34(C2×D43)⋊C4C2212yescomplemented
35C4⋊Dic43C2211yescharacteristic, complemented
36Dic43⋊C4C2212yescomplemented
37C23×C43C2311yescharacteristic
38C23×C43C2311yescharacteristic
39C22×D43—24no—
40C22×D43—24no—
41C22×D43—42no—
42C22×D43C2312yes—
43C22×D43C2312yes—
44D4×C43—22no—
45C2×C4×C43—22no—
46C2×C4×C43—22no—
47C2×C4×C43C2311yescharacteristic
48C2×C4×C43C2311yescharacteristic
49C2×C4×C43C2311yescharacteristic
50C2×C4×C43C2311yescharacteristic
51C2×C4×C43C2311yescharacteristic
52C22⋊D43—24no—
53C22⋊D43—42no—
54C2×Dic43C2312yes—
55C2×Dic43C2312yes—
56D172—24no—
57D172—22no—
58D172D414yescomplemented
59C4×D43—24no—
60C4×D43—42no—
61Dic86—22no—
62C22×C43—21no—
63C22×C43—21no—
64C22×C43—21no—
65C22×C43—21no—
66C22×C43—21no—
67C22×C43#4112yescomplemented
68C22×C43C2411yescharacteristic
69C2×D43—22no—
70C2×D43—22no—
71C2×D43—22no—
72C2×D43—22no—
73C2×D43—22no—
74C2×D43—48no—
75C2×D43C2×D414yes—
76C4×C43—21no—
77C4×C43—21no—
78C4×C43—21no—
79C4×C43—21no—
80C4×C43C2×D412yes—
81Dic43—22no—
82Dic43—22no—
83C2×C43—22no—
84C2×C43—41no—
85C2×C43C22×D411yescharacteristic
86C2×C43C2×#4111yescharacteristic
87C2×C43H(5,𝔽2)11yescharacteristic
88D43—24no—
89D43—42no—
90#546—431nomaximal, Sylow
91C43#54611yescharacteristic, complemented, Sylow
92C2×#41—431no—
93C22×D4—431no—
94#124—431no—
95#123—432no—
96C22⋊Q8—431no—
97#121—431no—
98#121—432no—
99#120—432no—
100C4×D4—431no—
101C4×D4D4311yescharacteristic, complemented
102C2×C22⋊C4—432no—
103C24—432no—
104#41—864no—
105C2×Q8—431no—
106C2×D4—432no—
107C2×D4—432no—
108C2×D4—431no—
109C2×D4—432no—
110C2×D4—431no—
111C2×D4—864no—
112C2×D4C2×D4311yescharacteristic
113C22×C4—432no—
114C22×C4—432no—
115C22×C4C2×D4311yescharacteristic
116C22×C4C2×D4311yescharacteristic, complemented
117C4⋊C4—431no—
118C4⋊C4—432no—
119C4⋊C4C2×D4311yescharacteristic, complemented
120C22⋊C4—432no—
121C22⋊C4—432no—
122C22⋊C4—432no—
123C22⋊C4—432no—
124C22⋊C4—432no—
125C22⋊C4C2×D4311yescharacteristic
126C22⋊C4C2×D4311yescharacteristic, complemented
127C42C2×D4311yescharacteristic, complemented
128C23—432no—
129C23—432no—
130C23—864no—
131C23—864no—
132C23—1722no—
133C23C22×D4311yescharacteristic
134C23C22×D4311yescharacteristic
135Q8—862no—
136D4—22no—
137D4—434no—
138D4—864no—
139D4—864no—
140D4—862no—
141D4—1722no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—432no—
145C2×C4—432no—
146C2×C4—864no—
147C2×C4—1722no—
148C2×C4C22×D4311yescharacteristic
149C2×C4C22×D4311yescharacteristic
150C2×C4C22×D4311yescharacteristic
151C2×C4C22×D4311yescharacteristic
152C2×C4C22×D4311yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—434no—
159C22—862no—
160C22—862no—
161C22—862no—
162C22—862no—
163C22—862no—
164C22—1728no—
165C22#1062189812yescomplemented
166C22C23×D4311yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—862no—
172C4—862no—
173C4D4×D4312yes—
174C2—22no—
175C2—41no—
176C2—864no—
177C2—1722no—
178C2C2×D4×D4311yescharacteristic
179C2C2×#1062189811yescharacteristic
180C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC4×D4×C43C2
hypercenterC4×D4D43
hypocenterC43#546
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10621898C2semidirect
2. C22×D172C2semidirect
3. #13063313C2semidirect
4. #13063310C2semidirect
5. #13063304C2semidirect
6. #13063299C2semidirect
7. #13063298C2semidirect
8. #13063293C2semidirect
9. C4×D172C2semidirect
10. C22⋊C4×D43C2semidirect
11. C4×D4×C43C2semidirect
15. C22×C4×C43C22semidirect
16. C2×C22⋊D43C22semidirect
17. C2×C22⋊D43C22semidirect
23. C2×C4×D43C22semidirect
24. C2×C4×D43C22semidirect
25. C2×Dic86C22semidirect
26. C4⋊C4×C43C22semidirect
28. C22⋊C4×C43C22semidirect
29. C42×C43C22semidirect
31. (C2×D43)⋊C4C22semidirect
32. (C2×D43)⋊C4C22semidirect
33. (C2×D43)⋊C4C22semidirect
34. (C2×D43)⋊C4C22semidirect
35. C4⋊Dic43C22semidirect
36. Dic43⋊C4C22semidirect
58. D172D4semidirect
67. C22×C43#41semidirect
91. C43#546semidirect
101. C4×D4D43semidirect
116. C22×C4C2×D43semidirect
119. C4⋊C4C2×D43semidirect
126. C22⋊C4C2×D43semidirect
127. C42C2×D43semidirect
165. C22#10621898semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106218982
C22×D1722
#130633132
#130633102
#130633042
#130632992
#130632982
#130632932
C4×D1722
C22⋊C4×D432
C4×D4×C432
#54643